Question Does a teaspoon of honey before bed really calm a child's cough? To test the folk remedy, pediatric researchers at Pennsylvania State University carried out a designed study involving a sample of 105 children who were ill with an upper respiratory tract infection. On the first night, parents rated their children's cough symptoms on a scale from O (no problems at all) to 30 (extremely severe). On the second night, the parents were instructed to give their sick child a dosage of liquid "medicine" prior to bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM)-an over-the-counter cough medicine-while others were given a similar dose of honey. Also, a third group of parents (the control group) gave their sick children no dosage at all. Again, the parents rated their children's cough symptoms, and the improvement in total cough symptoms score was deter-mined for each child. The data (improvement scores) for the study are shown in the following table. a. Find the median improvement score for the honey dosage group. b. Find the median improvement score for the DM dosage group. C. d. e. f. g. Find the median improvement score for the control group. Based on the results, parts a-c, what conclusions can paediatric researchers draw? Find the standard deviation of the improvement scores for the honey dosage group. Find the standard deviation of the improvement scores for the DM dosage group. h. Honey Dosage: 12 11 15 11 10 13 14 10 6 10 8 11 11 15 10 15 9 13 5 12 10 4 12 12 8 15 16 9 12 9 Find the standard deviation of the improvement scores for the control group. Based on the results, parts e-g, which group appears to have the most variability in coughing improvement scores? The least variability? 8 12 10 89 i. For each group, construct a box plot of the improvement scores. j. DM 469477 7 9 12 10 11 Do you detect any outliers in any of the three coughing improvement score distributions? 63 Dosage: 4 9 12 7 6 12 13 7 10 13 9 4 8 12 12 4 4 10 15 9 No Dosage (Control): 6 5 8 6 10 7 7 12 5 6 8 8 3 1 4 3 076 8 12 9 7 7 10 669 8 7 7 1 5 11 9 4 87